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Simplifying lg(x + 3) + lg(x + -3) = lg(6) Reorder the terms: gl(3 + x) + lg(x + -3) = lg(6) (3 * gl + x * gl) + lg(x + -3) = lg(6) (3gl + glx) + lg(x + -3) = lg(6) Reorder the terms: 3gl + glx + gl(-3 + x) = lg(6) 3gl + glx + (-3 * gl + x * gl) = lg(6) 3gl + glx + (-3gl + glx) = lg(6) Reorder the terms: 3gl + -3gl + glx + glx = lg(6) Combine like terms: 3gl + -3gl = 0 0 + glx + glx = lg(6) glx + glx = lg(6) Combine like terms: glx + glx = 2glx 2glx = lg(6) Reorder the terms for easier multiplication: 2glx = 6gl Solving 2glx = 6gl Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-6gl' to each side of the equation. -6gl + 2glx = 6gl + -6gl Combine like terms: 6gl + -6gl = 0 -6gl + 2glx = 0 Factor out the Greatest Common Factor (GCF), '2gl'. 2gl(-3 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'gl' equal to zero and attempt to solve: Simplifying gl = 0 Solving gl = 0 Move all terms containing g to the left, all other terms to the right. Simplifying gl = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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